Writing to the CEO with a follow-up (or threat to do so) to your local TV, Radio and Newspaper Consumer reporter usually works wonders. Your Congressman should be a bonus.

I love to fly Southwest and Alaska - never had problems, although recently on my flight home from Florida after performing on a Caribbean cruise, my guitar didn't arrive when the I and the rest of my luggage did.

I didn't panic or cause a fuss; I just filled out the appropriate papers and they said they'd call me when the guitar got in.
I got a call in the middle of the night that went like this:

"Hello. Mr. Kennedy? This is John from Southwest baggage. I'e got some good news for you."

"Great! My guitar arrived?"

"No. I just saved a bundle by switching to Geico!"

Well, I nearly wet the bed laughing, because they wouldn't be calling me in the middle of the night if the guitar hadn't arrived. Then he assured me that the guitar was in, it was undamaged and that he wanted to send it to the house right away by courier.

I told him to deliver it at a more respectable hour, thanked him and went back to sleep.
The guitar not arriving at the same time I did was as a result of my allowing myself to be bumped to a different flight to get a free flight some other time.

Seamus